Many contemporary problems within the Earth sciences are complex, and require an interdisciplinary approach. This book provides a comprehensive reference on data assimilation and inverse problems, as well as their applications across a broad range of geophysical disciplines. With contributions from world leading researchers, it covers basic knowledge about geophysical inversions and data assimilation and discusses a range of important research issues and applications in atmospheric and cryospheric sciences, hydrology, geochronology, geodesy, geodynamics, geomagnetism, gravity, near-Earth electron radiation, seismology, and volcanology. Highlighting the importance of research in data assimilation for understanding dynamical processes of the Earth and its space environment and for predictability, it summarizes relevant new advances in data assimilation and inverse problems related to different geophysical fields. Covering both theory and practical applications, it is an ideal reference for researchers and graduate students within the geosciences who are interested in inverse problems, data assimilation, predictability, and numerical methods.

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

A comprehensive reference on data assimilation and inverse problems, and their applications across a broad range of geophysical disciplines, ideal for researchers and graduate students. It highlights the importance of data assimilation for understanding dynamical processes of the Earth and its space environment, and summarises recent advances.

Data assimilation is the combination of information from observations and models of a particular physical system in order to get the best possible estimate of the state of that system. The technique has wide applications across a range of earth sciences, a major application being the production of operational weather forecasts. Others include oceanography, atmospheric chemistry, climate studies, and hydrology. Data Assimilation for the Earth System is a comprehensive survey of both the theory of data assimilation and its application in a range of earth system sciences. Data assimilation is a key technique in the analysis of remote sensing observations and is thus particularly useful for those analysing the wealth of measurements from recent research satellites. This book is suitable for postgraduate students and those working on the application of data assimilation in meteorology, oceanography and other earth sciences.

Data assimilation is an approach that combines observations and model output, with the objective of improving the latter. This book places data assimilation into the broader context of inverse problems and the theory, methods, and algorithms that are used for their solution. It provides a framework for, and insight into, the inverse problem nature of data assimilation, emphasizing ?why? and not just ?how.? Methods and diagnostics are emphasized, enabling readers to readily apply them to their own field of study. Readers will find a comprehensive guide that is accessible to nonexperts; numerous examples and diverse applications from a broad range of domains, including geophysics and geophysical flows, environmental acoustics, medical imaging, mechanical and biomedical engineering, economics and finance, and traffic control and urban planning; and the latest methods for advanced data assimilation, combining variational and statistical approaches.

Data assimilation methods were largely developed for operational weather forecasting, but in recent years have been applied to an increasing range of earth science disciplines. This book will set out the theoretical basis of data assimilation with contributions by top international experts in the field. Various aspects of data assimilation are discussed including: theory; observations; models; numerical weather prediction; evaluation of observations and models; assessment of future satellite missions; application to components of the Earth System. References are made to recent developments in data assimilation theory (e.g. Ensemble Kalman filter), and to novel applications of the data assimilation method (e.g. ionosphere, Mars data assimilation).

Data assimilation (DA) has been recognized as one of the core techniques for modern forecasting in various earth science disciplines including meteorology, oceanography, and hydrology. Since early 1990s DA has been an important s- sion topic in many academic meetings organized by leading societies such as the American Meteorological Society, American Geophysical Union, European G- physical Union, World Meteorological Organization, etc. nd Recently, the 2 Annual Meeting of the Asia Oceania Geosciences Society (AOGS), held in Singapore in June 2005, conducted a session on DA under the - tle of “Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications.” nd This rst DA session in the 2 AOGS was a great success with more than 30 papers presented and many great ideas exchanged among scientists from the three different disciplines. The scientists who participated in the meeting suggested making the DA session a biennial event. th Two years later, at the 4 AOGS Annual Meeting, Bangkok, Thailand, the DA session was of cially named “Sasaki Symposium on Data Assimilation for At- spheric, Oceanic and Hydrologic Applications,” to honor Prof. Yoshi K. Sasaki of the University of Oklahoma for his life-long contributions to DA in geosciences.